Completeness Theorems for Universal and Implicational Logics of Algebras Via Congruences

Labelled Sequent Calculi and Completeness Theorems for Implicational Relevant Logics

It is known that the implicational fragment of the relevant logic E is complete with respect to the class of Urquhart's models, where a model consists of a semilattice and a set of possible worlds. This paper shows that some implicational relevant logics, which are obtained from E by adding axioms, are complete with respect to the class of Urquhart's models with certain conditions. To show this...

A Syntactical Characterization of Structural Completeness for Implicational Logics

Implicational F-Structures and Implicational Relevance Logics

We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and proof-theoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all element...

Strong Completeness Theorems for Weak Logics of Common Belief

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.

Completeness-via-canonicity for coalgebraic logics

This thesis aims to provide a suite of techniques to generate completeness results for coalgebraic logics with axioms of arbitrary rank. We have chosen to investigate the possibility to generalize what is arguably one of the most successful methods to prove completeness results in ‘classical’ modal logic, namely completeness-via-canonicity. This technique is particularly well-suited to a coalge...